I've been to both Naval museum dozens of time over the years and USAF museum once. As the USAF visit was in the last year or so, I've give my impressions.
The USAF had more of a museum feel than the Navy one did. It felt like a lot more planning on plane location w/in the hangers had gone on. Not that the Navy felt cluttered, but it had more of a friendly vibe to it. There was very little invitation to touch the USAF aircraft as opposed to the Navy where you were very invited to touch and get close w/ the aircraft.
The Navy had more cockpits that you could climb into and see how well you would or wouldn't have fit in a fighter pit.
The USAF did, OTOH have a B2 that literally left me speechless. I did not realize until I was nose-to-nose-wheel with it how big of a beast that aircraft is.
The Navy, though, does have something the USAF museum does not have, and that is practice days for their demo team. You can go to the Naval Aviation Museum AND catch a practice session by the Blue Angels.
To truly appreciate what the USAF has would probably take a couple of full days, whereas the Navy one can be done in half a day or so.
They are both very good museums in their own rights, and I would suggest a visit to both. But if you could only visit one, Navy has my vote.